Question

Find the volume of the ellipsoid x^2+y^2+5z^2=100

Answer 1

I think I remember using a double integral to find these . . .

Answer 2

is the ans 200 pi sqrt(20) ?

Answer 3

no.

Answer 4

formula of an ellipsoid\[\left(\frac xa\right)^2+\left(\frac yb\right)^2+\left(\frac zc\right)^2=1\]
where \(a,b,c ,\) are the semi-principal axes
\[V_\text{{ellipsoid}}=\frac 43\pi abc\]

Answer 5

shouldnt it be

since area of ellipse at at z=0 is pi(a.b) and total width along z axis is 2sqrt(20)

should volume be area * width or 2pi.a.b.c @UnkleRhaukus
where am i going wrong?